The real-time nature of Twitter means that term distributions in tweets and in search queries change rapidly: the most frequent terms in one hour may look very different from those in the next. Informally, we call this phenomenon "churn". Our interest in analyzing churn stems from the perspective of real-time search. How do we "correctly" compute term statistics, considering that the underlying distributions change rapidly? In this paper, we present an analysis of tweet and query churn on Twitter, as a first step to answering this question. Analyses reveal interesting insights on the temporal dynamics of term distributions on Twitter and hold implications for the design of search systems.